It was the 20-year-old Wozniacki's first win of the year, following a straight-sets loss to Slovakia's Dominika Cibulkova at the Sydney International last week and exhibition losses to No. 2 Vera Zvonareva and Kim Clijsters at Singapore and Hong Kong.
Wozniacki didn't face a break point in the first set and converted her only chance. Dulko, the top-ranked doubles player, tested Wozniacki in the second set and pulled level at 4-4 with a service break, but the Danish player broke back immediately and served it out on her second match point after a double-fault on her first.
Wozniacki won six tournaments in 2010, including four of her last six, and can retain the top spot by making the semifinals here.
"My dream when I was a little girl was to reach No. 1 in the world, and that happened last year. But it's a new year, a new start," she said in a courtside interview. "I'm just looking forward to it."
In the earlier match on center court, Maria Sharapova won for the first time at Melbourne Park since taking the 2008 Australian Open title, beating Thai veteran Tamarine Tanasugarn 6-1, 6-3.
Former No. 1-ranked Sharapova, who missed the 2009 tournament because of a shoulder injury and was ousted in the first round last year by fellow Russian Maria Kirilenko, struggled with her serve and was inconsistent in the second set.
After losing the opening service game at love, Sharapova won seven straight games to take a 6-1, 1-0 lead.
The 33-year-old Tamarine, clearly not in peak physical condition, rallied and had a game point on serve for a 4-1 lead, but 14th-seeded Sharapova broke back and regained momentum, winning the last five games.
Even when she was winning, though, Sharapova had trouble finding range with her serve. She had 10 double-faults and five aces.
Nerves had a role in that.
"I definitely felt that in the beginning. I knew I had an early exit last year and didn't want that to happen this year," said Sharapova, who has the goal in Australia of "staying aggressive and little by little trying to get my game better, maybe to where it was a few years ago and maybe better than that."
French Open champion Francesca Schiavone had a couple of stutters before advancing with a 6-7 (4), 6-2, 6-4 victory over Arantxa Parra Santonja of Spain.
The sixth-seeded Schiavone had a chance to serve for the match at 5-3 in the third but was broken. The Italian player recovered quickly, breaking Parra Santonja's service in the next game to take the match.
In other women's first-round matches, No. 20 Kaia Kanepi of Estona beat Slovakia's Magdalena Rybarikova 2-6, 6-4, 6-3 and No. 29 Dominika Cibulkova of Slovakia advanced 6-2, 6-7 (4), 6-4 over Germany's Angelique Kerber.
No. 18 Sam Querrey was the first of the men's seeded players eliminated, losing 5-7, 6-2, 3-6, 6-1, 8-6 to Poland's Lukasz Kubot, while No. 12 Gael Monfils rallied from two sets and a break down to beat former world junior champion Thiemo De Bakker of the Netherlands.
De Bakker served for the match in the third set but made a series of unforced errors on key points and Monfils capitalized, winning 6-7 (5), 2-6, 7-5, 6-2, 6-1.
No. 26 Juan Monaco of Argentina advanced in straight sets over Simon Greul, who got a spot in the main draw earlier Monday when Julien Benneteau of France withdrew because of in infected finger on his playing hand.